Free-form deformation of solid geometric models
SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Generating blend surfaces using partial differential equations
Computer-Aided Design
Geometric and solid modeling: an introduction
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A butterfly subdivision scheme for surface interpolation with tension control
ACM Transactions on Graphics (TOG)
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Extended free-form deformation: a sculpturing tool for 3D geometric modeling
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Computer-Aided Design
Direct manipulation of free-form deformations
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
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Geometric modelling
Free-form deformations with lattices of arbitrary topology
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Wires: a geometric deformation technique
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Techniques for interactive design using the PDE method
ACM Transactions on Graphics (TOG)
Introduction to Implicit Surfaces
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Interactive shape design using volumetric implicit PDEs
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Dynamic PDE Surfaces with Flexible and General Geometric Constraints
PG '00 Proceedings of the 8th Pacific Conference on Computer Graphics and Applications
Linear algebra operators for GPU implementation of numerical algorithms
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Surface Representation Using Second, Fourth and Mixed Order Partial Differential Equations
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Scalar-field-guided adaptive shape deformation and animation
The Visual Computer: International Journal of Computer Graphics
Geometric Modeling
Temporal Computational Objects: A Process for Dynamic Surface Generation
ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing, Part II
Technical Section: Interactive free-form level-set surface-editing operators
Computers and Graphics
Solid modelling based on sixth order partial differential equations
Computer-Aided Design
Data structures for interactive high resolution level-set surface editing
Proceedings of Graphics Interface 2011
Facial geometry parameterisation based on Partial Differential Equations
Mathematical and Computer Modelling: An International Journal
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Parametric PDE techniques, which use partial differential equations (PDEs) defined over a 2D or 3D parametric domain to model graphical objects and processes, can unify geometric attributes and functional constraints of the models. PDEs can also model implicit shapes defined by level sets of scalar intensity fields. In this paper, we present an approach that integrates parametric and implicit trivariate PDEs to define geometric solid models containing both geometric information and intensity distribution subject to flexible boundary conditions. The integrated formulation of second-order or fourth-order elliptic PDEs permits designers to manipulate PDE objects of complex geometry and/or arbitrary topology through direct sculpting and free-form modeling. We developed a PDE-based geometric modeling system for shape design and manipulation of PDE objects. The integration of implicit PDEs with parametric geometry offers more general and arbitrary shape blending and free-form modeling for objects with intensity attributes than pure geometric models.